Given:
The equation is:
[tex](x-3)^2+2(x-3)-8=0[/tex]
To find:
The value of x.
Solution:
We have,
[tex](x-3)^2+2(x-3)-8=0[/tex]
Substitute [tex]x-3=u[/tex].
[tex]u^2+2u-8=0[/tex]
Splitting the middle term, we get
[tex]u^2+4u-2u-8=0[/tex]
[tex]u(u+4)-2(u+4)=0[/tex]
[tex](u-2)(u+4)=0[/tex]
Using zero product property, we get
[tex]u-2=0\text{ and }u+4=0[/tex]
[tex]u=2\text{ and }u=-4[/tex]
Now, substitute [tex]u=x-3[/tex].
[tex]x-3=2\text{ and }x-3=-4[/tex]
[tex]x=2+3\text{ and }x=-4+3[/tex]
[tex]x=5\text{ and }x=-1[/tex]
Therefore, the correct option is b.
The solutions to the equation are x = -1 and x = 5. The correct option is second option x = -1 and x = 5.
Quadratic equationFrom the question, we are to determine the solution of the given equation
(x - 3)² + 2(x - 3) - 8 = 0
First, we will expand the equation and clear the brackets
[tex](x - 3)^{2} + 2(x - 3) - 8 = 0[/tex]
[tex](x - 3)(x - 3) + 2(x - 3) - 8 = 0[/tex]
[tex]x^{2} -6x + 9 +2x - 6 - 8 = 0[/tex]
Simplifying
[tex]x^{2} -4x - 5 = 0[/tex]
Factorizing, we get
[tex]x^{2} -5x +x- 5 = 0[/tex]
[tex]x(x-5)+1(x- 5) = 0[/tex]
[tex](x+1)(x-5)= 0[/tex]
Then,
x + 1 = 0 or x - 5 = 0
x = -1 or x = 5
Hence, the solutions to the equation are x = -1 and x = 5. The correct option is second option x = -1 and x = 5.
Learn more on solving Quadratic equations here: https://brainly.com/question/8649555
Please help 30 points
a+b=8
3a - 45=3
And is it good for the elimination method
Answer: a is 16, b is -8
Step-by-step explanation:
3a-45=3
add 45 to both sides to get rid of -45
3a=48
divide both sides by 3
a = 16
plug 16 into the first equation
16 + b = 8
subtract 16 from both sides
b = -8
is it good for the elimination method? hmm i probably wouldn't use it in this case since there aren't any variables to cancel out.
Write b increased by .17 as an expression in the box.
Answer:
b+.17
Step-by-step explanation:
I NEED HELP PLEASE- ‼️‼️‼️
Answer:
18x^2 - 30x
Step-by-step explanation:
Distribution:
You just have to distribute 6x by each term in the parenthesis.
Equation: 6x(3x-5)
(You can also think of it as: 6x * 3x + 6x * -5)
18x^2 - 30x
This is as simplified as can it can be.
(You can’t add terms that have different variables, seeing as the first term has x^2 and the second one only has x).
One card is drawn at random from a deck of cards. What is the probability that the card will be a red ace?
Answer:
Since a normal deck of cards holds 52 cards, and there are two red aces, ace of diamonds and ace of hearts. So 2/52 probability that you will draw a red ace, to simplify it is a 3.84% chance of drawing a red ace.
Find the volume of the figure. Use 3.14 for pi
Answer:
1494.64
Step-by-step explanation:
Divide 28 by 2 = 14
14 times 3.14 times 34
I hope thats right
Mary is designing a square garden in her field to grow vegetables. The minimum size for a garden is 2 meters on each side. She decides it would be best to have each side be 2 meters long plus an additional x amount of meters.
a. What expression can represent the area of the garden?
b. Mary’s five additional friends also want to make this garden with the same dimen
What is the most accurate definition for FACTORS?
Answer:
A number that can go into another number without a remainder.
Step-by-step explanation:
Answer:
actor definition, one of the elements contributing to a particular result or situation: Poverty is only one of the factors in crime.
please answer the one that says PART B:) thanks (i’ll give brainliest)
Answer:
She is not correct
Step-by-step explanation:
When you add them together and divide by 1 7/8 (1.875), It does not come out evenly.
If you can help me I would be very thankful!
Answer:
4x + 2.5y = 184
x = y - 6
Step-by-step explanation:
Let the number of smoothies sold by stand = x
And number of cones sold = y
If the selling price of each cone = $2.5
Selling price of the 'y' cones = $2.5y
Selling price of each smoothies = $4
Then sales of smoothies = $4x
If the total sales of one day = $184
Equation for this situation will be,
4x + 2.5y = 184 -------(1)
If the stand sold 6 less smoothies than the cones,
x = y - 6 -----(2)
Therefore, system of equations contains two equations (1) and (2).
Jasmine made a line plot to show the lengths of string in inches that the art teacher gave her for a craft project
Which of the following statements that Jasmine made about the string lengths are true? Select all that apply.
A. The difference between the longest length and shortest length is 14 inches.
B .I have twice as many 12-inch strings as I do 8-inch strings.
C. The total length of string that I have is 84 inches.
D. I cannot determine what the shortest string is by looking at my line plot.
E. Since I need 100 total inches of string for my project, I have enough string.
WILL GIVE BRAINLEST
Answer:
B and C
Step-by-step explanation:
I took a test
Answer:
answer is b and c
Step-by-step explanation:
When writing the inequatlity for the following situation, what value will be the coefficient?
Isabella is going roller skating. To rent skates, there is a $3 fee. For every hour she wants to skate, it costs $1.25. Isabella does
not want to spend more than $12. Write an inequality to determine how many hours Isabella can skate.
Answer: y = 1.25x + 3
Step-by-step explanation: Hope I helped!
Answer:
7 h
Step-by-step explanation:
12-3=9
9÷1.25=7.2
I saw a rectangular floor is 42 M long and 39 meters wide how many square meters of flooring do they need ?
Answer: 81 I guess
Step-by-step explanation: (empty)
Answer:
1,638
Step-by-step explanation:
Area equation=Lenngth*Width
42*39=1,638sq. M
I will give brainliest!! Pls help!!!
I uploaded the answer to a file hosting. Here's link:
bit.[tex]^{}[/tex]ly/3a8Nt8n
Nick used his credit card to make several large purchases, and now owes the credit card company $4,273 plus 32% interest. His mother gave him $500 for his birthday. Which is the most responsible choice he can make regarding his birthday money?
A.
He can use all the money to pay down his credit card debt.
B.
He can invest $200 in the stock market and pay down his credit card debt with the rest.
C.
He can put $250 into a savings account that pays 3.8% interest and pay down his credit card debt with the rest.
D.
He can put all the birthday money in the 3.8% savings account.
Answer:
Step-by-step explanation:
A, because more debt would build up for your credit card if you added money to a savings account since you would have to wait a whole year to get interest back. And it wouldn't be B because it simply would not be worth it to invest in stocks while in debt. Also, I just took the test and got it right!
What is the value of x in the diagram?
A right angled triangle with base 2x+2, altitude x and hypotenuse 2x+3.
Answer:
x = 5
Step-by-step explanation:
x² + (2x+2)² = (2x+3)²
x² + 4x² + 8x + 4 = 4x² + 12x + 9
x² - 4x - 5 = 0
(x - 5)(x + 1) = 0
x = -1 This can be discounted as the answer because you cannot have a negative length
answer: x = 5
list all the equivalent fractions for the 12/20
Answer:
6/10
9/15
12/20
Step-by-step explanation:
Answer: 6/10, 3/5
Hope it helps!
Identify the place of the
3
in 24.936
Answer:
hundredths place
Step-by-step explanation:
When using decimals we determine by
Tens,ones.Hundredths,Thousandths, etc
Answer:
Hundredths Place
Step-by-step explanation:
Find the volume of a pyramid with a square base, where the perimeter of the base is
18.5 ft and the height of the pyramid is 7.6 ft. Round your answer to the nearest
tenth of a cubic foot.
Answer:
132 cm. 3. 3. a rectangular pyramid with a height of 5.2 meters and a base 8 ... 7. an oblique cone with a height of 10.5 millimeters and a radius of 1.6 ... base is about 15,400 square feet, find the volume of air that the ... ANSWER: 32.2 ft. 3. Find the volume of each solid. Round to the nearest tenth. eSolutions ...
Step-by-step explanation:
Can yall pls answer just number 2 for me pls Its due late and im rlly tryna make up my work ill definetly give brainliest just pls : (
Answer:
24y + 16
Step-by-step explanation:
If your searching for number 2 itself, the answer will be 24y + 16, because because you have to multily whats out of the brackets by whats in the brackets. 3y+2 is in the brackets so 8 times whats in the braackets gives u the answer.
Which statement about the graph of y = 1/3(2/3)^x is true?
A The graph has a vertical asymptote.
B The graph crosses the y-axis at (0,7).
C The graph has an asymptote aty 1 3
D The graph decreases from left to right.
Plz help
Answer: the answer D is correct and is proven to be correct
Step-by-step explanation:
One hundred tomato plants were randomly selected from a large garden, and a 90% confidence interval was computed to determine the true proportion of plants that produce useable tomatoes. The interval is 0.86 to 0.92.
What would happen to the width of the confidence interval if the confidence level increased to 95%?
Answer:
The width of the interval would increase.
Step-by-step explanation:
What is 5 1/6 + 2/3?
The sum of the fraction 5 1/6+2/3 is 5.83.
How to calculate sum of the fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. When expressed in common English, a fraction, such as one-half, eight-fifths, or three-quarters, specifies the number of components of a specific size.
5 1/6 + 2/3 = 5.83
An element of a whole is a fraction. When expressed in common English, a fraction, such as one-half, eight-fifths, or three-quarters, specifies the number of components of a specific size. A fraction appears in the numerator or denominator of a complex fraction.
There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its types based on these two terms. The terminology used to calculate fractions the parts of a whole object.
To learn more about fraction refer to:
https://brainly.com/question/17220365
#SPJ1
A shop sells bag of peanuts for two dollars and a bag of walnuts for five dollars at nine bags of purchase for total cost of $36 how many bag of walnuts were purchased purchased
The midsegment of aABC is IM. What is the length of AB If IB is 14 inches
long?
B
А
M
A
С
A. 56 inches
B. 7 inches
C. 28 inches
D. 14 inches
y / 4 + 8 = 22 Answer?
Answer:
y = 3.5
Step-by-step explanation:
First, you do 14/4 which = 3.5
Hope this helps!
Answer:
y/4+8=22
y/4=22-8
y/4=14/1
y=56
Quel est la vitesse moyenne de 108 km/h en m/s
Answer:
108 km/h = 30 m/s
Step-by-step explanation:
1 km = 1,000 m, 1 hr = 3,600 sec.
108 × 5 ÷ 18 = 30
Answer:
En effet, 108 km/h = 30 m/s
Step-by-step explanation:
mais pourquoi la question est-elle en fr ?
Solve for x.
ax + bx = 10
3. Identify the pair of angles as complementary, supplementary, both, or neither.
a. supplementary
b. complementary and supplementary
c. neither
d. complementary
Answer:
D) Complementary
Step-by-step explanation:
Angles are complementary if they add up to 90°. The image shown showcases that the angles are 90° because of the box on the corner.
Supplementary means it adds up to 180° which would be a straight line, this is not the case where this is shown.
Kelly is attending physical therapyCB after knee surgery he walked 9 1/4 miles over 3 days how many miles is the per day simplilfy the answer as a mixed number
Answer:
The miles per day are: 3 1/12.
Step-by-step explanation:
With the information provided, in order to find the miles per day you have to divide the number of miles he walked by 3 that is the number of days:
9 1/4÷3
In order to solve this, first you have to convert the mixed number to an improper fraction by multiplying the denominator for the whole number, add the numerator and this would be divided by the denominator:
(4*9)+1/4
36+1/4
37/4
Now, you divide this by 3:
37/4÷3
37/(4*3)
37/12
You can conver this fraction into a mixed number by dividing 37 by 12. 12 goes into 37 three times which would be the whole number. Then, three times 12 is 36 and the remainder is 1. So, 1 would be the numerator and the denominator stays th same which is 12. The mixed number is: 3 1/12.
According to this, the answer is that the miles per day are: 3 1/12.
